Monoclonal antibodies (mAbs) targeting the influenza hemagglutinin (HA) can be used as prophylactics or templates for next-generation vaccines. Here, we isolated broad, subtype-neutralizing mAbs from human B cells recognizing the H1 or H3 HA "head" and a mAb engaging the conserved stem. The H1 mAbs bind the lateral patch epitope on HAs from 1933 to 2021 and a prepandemic swine H1N1 virus. We improved neutralization potency using directed evolution toward a contemporary H1 HA. Deep mutational scanning of four antigenically distinct H1N1 viruses identified potential viral escape pathways. For the H3 mAbs, we used cryo-electron microscopy to define their epitopes: One mAb binds the side of the HA head, accommodating the N133 glycan and a pocket underneath the receptor binding site; the other mAb recognizes an HA stem epitope that partially overlaps with previously characterized mAbs but with distinct antibody variable genes. Collectively, these mAbs identify conserved sites recognized by broadly-reactive mAbs that may be elicited by next-generation vaccines.